This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some...

To keep the key idea of rough set and the representation of information in rough set theory, empty representation is processed properly and three new forms of rough approximation sets are defined as a generation of general binary relation based rough set model. Moreover, the properties of approximation operators in these new rough sets are discussed. The relations among them are studied in this...

Article history: Received 15 July 2009 Received in revised form 6 April 2010 Accepted 7 April 2010 Available online 9 April 2010

The collection of the rough set pairs of an approximation (U, R) can be made into a Stone algebra by defining two binary operators and one unary operator on the pairs. By introducing a more unary operator, one can get a regular double Stone algebra to describe the rough set pairs of an approximation space. Sequent calculi corresponding to the rough alg...